<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\problem{Enclosure Area}

No one really knew how rich old Mr. Miserly really was. People used to
joke about how he must own half the town, but it was not until he
passed away that people discovered that he was the sole owner of the
town's banks. Since most of the homes and small businesses had
mortgages with those banks, he really did own half the town.

No one really knew how civic-minded Mr. Miserly really was. But the
day after his will was read, the townsfolk woke to the sound of
workmen hammering wooden stakes into the ground near every building
that was partly owned by the banks. Each family found, in their
mailbox, a small green flag and a leaflet with these instructions:

~
 
\begin{quotation}
\noindent
\textit{From:} the executors of the Miserly estate

~

You may tie this flag to any of the wooden stakes in the town.  At
noon, the executors will tie strings from one flagged stake to
the next, forming the shortest path they can make that encloses {\em all}
the flagged stakes. [The high school's Geometry teacher tried to
explain to people that this formed a convex polygon, but no one paid
much attention.]

Any building inside the perimeter will have its mortgage paid off by
the Miserly estate.

Furthermore, the estate will donate 
\$1 to the Municipal Fund for every square ILMU\footnote{Imaginary 
Linear Measurement Unit} of area within the enclosed perimeter.

\end{quotation}


Most of the townsfolk never got as far as reading the final paragraph
before rushing off to place their flag near their home or family
business.

You, however, held on to your flag. You now have the last flag.  You
can see that your own home is safe, surrounded by the flags of your
neighbors. So your thoughts turn to the donation to the Municipal
Fund.  You want to place your flag where it will increase the enclosed
area to the largest possible value.


\subsection*{Input}

The first line of input contains two integers $n$ and $k$, where $n$
is the number of stakes in the forest and $k$ is the number of stakes with flags already tied to them. $3 \leq k &lt; n \leq \num{100000}$

The next $n$ lines each have two integers $x$ and $y$,
$\num{-1000000000} \leq x, y \leq \num{1000000000}$,
specifying the location of each stake, measured in ILMUs. The first $k$ of
these are the stakes already flagged by the townspeople.

\begin{itemize}

\item Assume that any two stakes can be joined by a straight length of
string, ignoring any possible interference from buildings, trees, or
other physical objects.

\item There may be unflagged stakes both within and without 
the current perimeter.

\item No three stakes will occupy co-linear locations.
\end{itemize}


\subsection*{Output}

Print a single line containing a floating point number denoting the
maximum area you can achieve by gaining flagging one additional
stake. Print this to one decimal place of precision.

\section*{Time Limit}

Solutions to this problem must run in no more than 6 seconds.


\subsection*{Example}

\begin{center}
  \begin{tabular}{|p{0.45\linewidth}|p{0.45\linewidth}|}
    \multicolumn{1}{l}{\textbf{Sample Input}} &amp;
    \multicolumn{1}{l}{\textbf{Sample Output}} \\

    \hline \noalign{\vskip 0.25em}
\begin{minipage}{\textwidth}

\verbfile{Enclosure/judgeData/EnclosureArea-0001.in}

\end{minipage}
&amp;
\begin{minipage}{\textwidth}

\verbfile{Enclosure/judgeData/EnclosureArea-0001.ans}

\end{minipage} \\
  \noalign{\vskip 0.25em}  \hline \noalign{\vskip 0.25em}



\begin{minipage}{\textwidth}

\verbfile{Enclosure/judgeData/EnclosureArea-1100.in}

\end{minipage}
&amp;
\begin{minipage}{\textwidth}

\verbfile{Enclosure/judgeData/EnclosureArea-1100.ans}

\end{minipage} \\
  \noalign{\vskip 0.25em}  \hline \noalign{\vskip 0.25em}



\end{tabular}
\end{center}

</pre></body></html>